{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# How to size your bets - The Kelly Rule"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "he Kelly rule has a long history in gambling because it provides guidance on how much to stake on each of an (infinite) sequence of bets with varying (but favorable) odds to maximize terminal wealth. It was published as A New Interpretation of the Information Rate in 1956 by John Kelly who was a colleague of Claude Shannon's at Bell Labs. He was intrigued by bets placed on candidates at the new quiz show The $64,000 Question, where a viewer on the west coast used the three-hour delay to obtain insider information about the winners. \n",
    "\n",
    "Kelly drew a connection to Shannon's information theory to solve for the bet that is optimal for long-term capital growth when the odds are favorable, but uncertainty remains. His rule maximizes logarithmic wealth as a function of the odds of success of each game, and includes implicit bankruptcy protection since log(0) is negative infinity so that a Kelly gambler would naturally avoid losing everything."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-17T16:14:00.120495Z",
     "start_time": "2020-06-17T16:14:00.116620Z"
    }
   },
   "outputs": [],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings('ignore')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-17T16:14:01.985085Z",
     "start_time": "2020-06-17T16:14:00.122715Z"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "from pathlib import Path\n",
    "\n",
    "import numpy as np\n",
    "from numpy.linalg import inv\n",
    "from numpy.random import dirichlet\n",
    "import pandas as pd\n",
    "\n",
    "from sympy import symbols, solve, log, diff\n",
    "from scipy.optimize import minimize_scalar, newton, minimize\n",
    "from scipy.integrate import quad\n",
    "from scipy.stats import norm\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-17T16:14:01.993429Z",
     "start_time": "2020-06-17T16:14:01.986757Z"
    }
   },
   "outputs": [],
   "source": [
    "sns.set_style('whitegrid')\n",
    "np.random.seed(42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-17T16:14:02.004157Z",
     "start_time": "2020-06-17T16:14:01.995813Z"
    }
   },
   "outputs": [],
   "source": [
    "DATA_STORE = Path('..', 'data', 'assets.h5')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The optimal size of a bet"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Kelly began by analyzing games with a binary win-lose outcome. The key variables are:\n",
    "- b: The odds define the amount won for a \\\\$1 bet. Odds = 5/1 implies a \\\\$5 gain if the bet wins, plus recovery of the \\\\$1 capital.\n",
    "- p: The probability defines the likelihood of a favorable outcome.\n",
    "- f: The share of the current capital to bet.\n",
    "- V: The value of the capital as a result of betting.\n",
    "\n",
    "The Kelly rule aims to maximize the value's growth rate, G, of infinitely-repeated bets (see Chapter 5 for background).\n",
    "$$G=\\lim_{N\\rightarrow\\infty}=\\frac{1}{N}\\log\\frac{V_N}{V_0}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can maximize the rate of growth G by maximizing G with respect to f, as illustrated using sympy as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-17T16:14:02.567780Z",
     "start_time": "2020-06-17T16:14:02.005902Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(odds*probability + probability - 1)/odds]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "share, odds, probability = symbols('share odds probability')\n",
    "Value = probability * log(1 + odds * share) + (1 - probability) * log(1 - share)\n",
    "solve(diff(Value, share), share)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-17T16:14:02.633575Z",
     "start_time": "2020-06-17T16:14:02.573409Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[2*p - 1]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f, p = symbols('f p')\n",
    "y = p * log(1 + f) + (1 - p) * log(1 - f)\n",
    "solve(diff(y, f), f)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Get S&P 500 Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-17T16:14:02.792236Z",
     "start_time": "2020-06-17T16:14:02.651447Z"
    }
   },
   "outputs": [],
   "source": [
    "with pd.HDFStore(DATA_STORE) as store:\n",
    "    sp500 = store['sp500/stooq'].close"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Compute Returns & Standard Deviation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-17T16:14:02.832855Z",
     "start_time": "2020-06-17T16:14:02.807802Z"
    }
   },
   "outputs": [],
   "source": [
    "annual_returns = sp500.resample('A').last().pct_change().dropna().to_frame('sp500')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-17T16:14:02.862566Z",
     "start_time": "2020-06-17T16:14:02.846587Z"
    }
   },
   "outputs": [],
   "source": [
    "return_params = annual_returns.sp500.rolling(25).agg(['mean', 'std']).dropna()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-17T16:14:02.908127Z",
     "start_time": "2020-06-17T16:14:02.877414Z"
    }
   },
   "outputs": [],
   "source": [
    "return_ci = (return_params[['mean']]\n",
    "                .assign(lower=return_params['mean'].sub(return_params['std'].mul(2)))\n",
    "                .assign(upper=return_params['mean'].add(return_params['std'].mul(2))))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-17T16:14:04.295279Z",
     "start_time": "2020-06-17T16:14:02.914036Z"
    },
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1008x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "return_ci.plot(lw=2, figsize=(14, 8))\n",
    "plt.tight_layout()\n",
    "sns.despine();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Kelly Rule for a Single Asset - Index Returns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In a financial market context, both outcomes and alternatives are more complex, but the Kelly rule logic does still apply. It was made popular by Ed Thorp, who first applied it profitably to gambling (described in Beat the Dealer) and later started the successful hedge fund Princeton/Newport Partners.\n",
    "\n",
    "With continuous outcomes, the growth rate of capital is defined by an integrate over the probability distribution of the different returns that can be optimized numerically.\n",
    "We can solve this expression (see book) for the optimal f* using the `scipy.optimize` module:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-17T16:14:04.305225Z",
     "start_time": "2020-06-17T16:14:04.297732Z"
    }
   },
   "outputs": [],
   "source": [
    "def norm_integral(f, mean, std):\n",
    "    val, er = quad(lambda s: np.log(1 + f * s) * norm.pdf(s, mean, std), \n",
    "                               mean - 3 * std, \n",
    "                               mean + 3 * std)\n",
    "    return -val"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-17T16:14:04.341592Z",
     "start_time": "2020-06-17T16:14:04.307745Z"
    }
   },
   "outputs": [],
   "source": [
    "def norm_dev_integral(f, mean, std):\n",
    "    val, er = quad(lambda s: (s / (1 + f * s)) * norm.pdf(s, mean, std), m-3*std, mean+3*std)\n",
    "    return val"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-17T16:14:04.349405Z",
     "start_time": "2020-06-17T16:14:04.343810Z"
    }
   },
   "outputs": [],
   "source": [
    "def get_kelly_share(data):\n",
    "    solution = minimize_scalar(norm_integral, \n",
    "                        args=(data['mean'], data['std']), \n",
    "                        bounds=[0, 2], \n",
    "                        method='bounded') \n",
    "    return solution.x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-17T16:14:18.112626Z",
     "start_time": "2020-06-17T16:14:04.350939Z"
    }
   },
   "outputs": [],
   "source": [
    "annual_returns['f'] = return_params.apply(get_kelly_share, axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-17T16:14:19.387162Z",
     "start_time": "2020-06-17T16:14:18.114035Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x576 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "return_params.plot(subplots=True, lw=2, figsize=(14, 8));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-17T16:14:19.403789Z",
     "start_time": "2020-06-17T16:14:19.388563Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sp500</th>\n",
       "      <th>f</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2015-12-31</th>\n",
       "      <td>-0.007266</td>\n",
       "      <td>1.999996</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-12-31</th>\n",
       "      <td>0.095350</td>\n",
       "      <td>1.999996</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-12-31</th>\n",
       "      <td>0.194200</td>\n",
       "      <td>1.999996</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-12-31</th>\n",
       "      <td>-0.062373</td>\n",
       "      <td>1.999996</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2019-12-31</th>\n",
       "      <td>0.288781</td>\n",
       "      <td>1.999996</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               sp500         f\n",
       "Date                          \n",
       "2015-12-31 -0.007266  1.999996\n",
       "2016-12-31  0.095350  1.999996\n",
       "2017-12-31  0.194200  1.999996\n",
       "2018-12-31 -0.062373  1.999996\n",
       "2019-12-31  0.288781  1.999996"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "annual_returns.tail()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Performance Evaluation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-17T16:14:20.298149Z",
     "start_time": "2020-06-17T16:14:19.409631Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "(annual_returns[['sp500']]\n",
    " .assign(kelly=annual_returns.sp500.mul(annual_returns.f.shift()))\n",
    " .dropna()\n",
    " .loc['1900':]\n",
    " .add(1)\n",
    " .cumprod()\n",
    " .sub(1)\n",
    " .plot(lw=2));\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-17T16:14:20.324414Z",
     "start_time": "2020-06-17T16:14:20.309663Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    45.000000\n",
       "mean      1.979025\n",
       "std       0.062282\n",
       "min       1.708206\n",
       "25%       1.999996\n",
       "50%       1.999996\n",
       "75%       1.999996\n",
       "max       1.999996\n",
       "Name: f, dtype: float64"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "annual_returns.f.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-17T16:14:20.353968Z",
     "start_time": "2020-06-17T16:14:20.330832Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>lower</th>\n",
       "      <th>upper</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1975-12-31</th>\n",
       "      <td>0.076574</td>\n",
       "      <td>-0.289442</td>\n",
       "      <td>0.442591</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1976-12-31</th>\n",
       "      <td>0.077649</td>\n",
       "      <td>-0.289600</td>\n",
       "      <td>0.444897</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1977-12-31</th>\n",
       "      <td>0.068336</td>\n",
       "      <td>-0.306402</td>\n",
       "      <td>0.443074</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1978-12-31</th>\n",
       "      <td>0.071410</td>\n",
       "      <td>-0.299973</td>\n",
       "      <td>0.442794</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1979-12-31</th>\n",
       "      <td>0.058325</td>\n",
       "      <td>-0.278930</td>\n",
       "      <td>0.395581</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                mean     lower     upper\n",
       "Date                                    \n",
       "1975-12-31  0.076574 -0.289442  0.442591\n",
       "1976-12-31  0.077649 -0.289600  0.444897\n",
       "1977-12-31  0.068336 -0.306402  0.443074\n",
       "1978-12-31  0.071410 -0.299973  0.442794\n",
       "1979-12-31  0.058325 -0.278930  0.395581"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "return_ci.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Compute Kelly Fraction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-17T16:14:20.366598Z",
     "start_time": "2020-06-17T16:14:20.358919Z"
    }
   },
   "outputs": [],
   "source": [
    "m = .058\n",
    "s = .216"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-17T16:14:20.558825Z",
     "start_time": "2020-06-17T16:14:20.372938Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimal Kelly fraction: 1.1974\n"
     ]
    }
   ],
   "source": [
    "# Option 1: minimize the expectation integral\n",
    "sol = minimize_scalar(norm_integral, args=(m, s), bounds=[0., 2.], method='bounded')\n",
    "print('Optimal Kelly fraction: {:.4f}'.format(sol.x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-17T16:14:20.689150Z",
     "start_time": "2020-06-17T16:14:20.564571Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimal Kelly fraction: 1.1974\n"
     ]
    }
   ],
   "source": [
    "# Option 2: take the derivative of the expectation and make it null\n",
    "x0 = newton(norm_dev_integral, .1, args=(m, s))\n",
    "print('Optimal Kelly fraction: {:.4f}'.format(x0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Kelly Rule for Multiple Assets"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will use an example with various equities. [E. Chan (2008)](https://www.amazon.com/Quantitative-Trading-Build-Algorithmic-Business/dp/0470284889) illustrates how to arrive at a multi-asset application of the Kelly Rule, and that the result is equivalent to the (potentially levered) maximum Sharpe ratio portfolio from the mean-variance optimization. \n",
    "\n",
    "The computation involves the dot product of the precision matrix, which is the inverse of the covariance matrix, and the return matrix:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-17T16:14:29.776363Z",
     "start_time": "2020-06-17T16:14:20.702939Z"
    }
   },
   "outputs": [],
   "source": [
    "with pd.HDFStore(DATA_STORE) as store:\n",
    "    sp500_stocks = store['sp500/stocks'].index \n",
    "    prices = store['quandl/wiki/prices'].adj_close.unstack('ticker').filter(sp500_stocks)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-17T16:14:29.815295Z",
     "start_time": "2020-06-17T16:14:29.781800Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "DatetimeIndex: 14277 entries, 1962-01-02 to 2018-03-27\n",
      "Columns: 482 entries, MMM to ZTS\n",
      "dtypes: float64(482)\n",
      "memory usage: 52.6 MB\n"
     ]
    }
   ],
   "source": [
    "prices.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-17T16:14:29.885865Z",
     "start_time": "2020-06-17T16:14:29.820248Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "DatetimeIndex: 359 entries, 1988-02-29 to 2017-12-31\n",
      "Freq: M\n",
      "Columns: 207 entries, MMM to XRX\n",
      "dtypes: float64(207)\n",
      "memory usage: 583.4 KB\n"
     ]
    }
   ],
   "source": [
    "monthly_returns = prices.loc['1988':'2017'].resample('M').last().pct_change().dropna(how='all').dropna(axis=1)\n",
    "stocks = monthly_returns.columns\n",
    "monthly_returns.info()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Compute Precision Matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-17T16:14:29.912462Z",
     "start_time": "2020-06-17T16:14:29.891500Z"
    }
   },
   "outputs": [],
   "source": [
    "cov = monthly_returns.cov()\n",
    "precision_matrix = pd.DataFrame(inv(cov), index=stocks, columns=stocks)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-17T16:14:29.921595Z",
     "start_time": "2020-06-17T16:14:29.916844Z"
    }
   },
   "outputs": [],
   "source": [
    "kelly_allocation = monthly_returns.mean().dot(precision_matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-17T16:14:29.952429Z",
     "start_time": "2020-06-17T16:14:29.934090Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    207.000000\n",
       "mean       0.237375\n",
       "std        3.470213\n",
       "min      -11.586454\n",
       "25%       -1.750238\n",
       "50%        0.093455\n",
       "75%        2.505289\n",
       "max        9.255888\n",
       "dtype: float64"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kelly_allocation.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-17T16:14:29.968235Z",
     "start_time": "2020-06-17T16:14:29.957817Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "49.13669441959205"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kelly_allocation.sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Largest Portfolio Allocation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The plot shows the tickers that receive an allocation weight > 5x their value:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-17T16:14:30.574792Z",
     "start_time": "2020-06-17T16:14:29.974399Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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6tCRp2LBhGjRokHbv3q3du3dryZIlWrJkiVavXq2oqKgKv9flctn+x83j8di+jYAZcJxZB+Oi9VSlzwy/RPWD/v37a/369crOzlZqampoeUlJibKzs/Xpp5+qe/fu6t69u06ePKnXX39dfr9fn376qV5++WU1bNhQycnJmjx5sjZu3CiHw6EPP/zQwBYBAACjmOIMjiSlpqZq0KBBatSokV577bXQ8k2bNqlRo0baunVr6Ibh7777TsnJydqyZYs6duyoxYsX69prr9X1118vSTp58qQKCwvLnQUCAAB1h2kCTmxsrFq3bq2oqCg1atQotHzFihUaPnx4uaehfvKTnygtLU3Lli3TmjVrtHDhQj3//PP6+uuv5XK5FBUVpRkzZqhVK16+BQBAXeQIBoNBo4swSl24DlsX2ngl8KI/VAcv+rMWxkXrqUqfmeYMDmAUr7+MHyhUS1GJTw0iXUaXAeAcprnJGDCKO9xcL4Pk8VXrOXY0z+gSAJyHgAMAAGyHgAMAAGyHgAMAAGyHgAMAAGyHgAMAAGyHgAMAAGyHgAMAAGyHgAMAAGyHgAMAAGyHgANcJq+/rEb3zxw51tMyjol9AbNhLirgMrnDnUzOiXKYywwwH1MFnL1792rOnDn69ttvFQwG9fOf/1yPP/64IiMj1a9fP+3Zs+eCbRYsWKD/+Z//UWxsrILBoPx+v9q3b69p06apYcOGBrQCAAAYzTSXqEpLSzV69Gilp6crJydHGzZsUL9+/TRy5EgFAoFKt+3bt6+ys7O1fv16bdiwQUVFRVq+fHktVQ4AAMzGNGdwSkpKdObMGRUXF4eW9e/fXw0bNlRZ2aXf8+Dz+VRcXKymTZvWRJkAAMACTBNwoqOjNWnSJI0YMUI//elP1blzZ3Xp0kW33367vvnmm0q33bRpkz799FMFAgF99dVXuuqqq3Tbbbdd9Dt9Pp88Hs+VaoIpeb1e27extnETMH4Mx5l1MC5aT2V9VtGY7AgGg8GaLOpyFRYWavfu3dq9e7fee+89SdK8efN0zz33VHgPzqlTp/T0009Lkvx+v/7whz/oq6++0iuvvFLpd3k8Htv/WNWFNhqBm4xxLm4ythbGReupSp+Z5h6cTz/9VC+//LIaNmyo5ORkTZ48WRs3bpTD4dCHH354yfsJDw/XkCFDtHv37hqsFgAAmJlpAk5MTIwWL16sTz75JLTs5MmTKiwsVHJy8mXt64MPPlBiYuKVLhEAAFiEae7Bufrqq7Vw4UI9//zz+vrrr+VyuRQVFaUZM2YoIiJCxcXFSkpKKrfNm2++Ken/7sFxOBzy+Xxq0aKFZs6caUQzAACACZgm4EjSjTfeqBtvvPFHPzt48OCPLo+Pj9fDDz9ck2UBAACLMVXAAazA6y/jplKUU1TiU4NIl9FlADiHae7BAazCHe6s0f3z+Kr1HDuaZ3QJAM5DwAEAALZDwAEAALZDwAEAALZDwAEAALZDwAEAALZDwAEAALZDwAEAALZDwAEAALZDwAEAALZDwAFqgNdfVuVtExISrmAlqA0t41oZXQKA8zAXFVAD3OFOxaVvNLoM1BLmJgPMx5CAk5+frx49euiGG27Q66+/Xu6z9PR0vf3229q5c6e6du2qtm3bKiwsTA6HQyUlJWrYsKEyMzPVqVMnSVJxcbEWLFig7du3KyIiQpLUvXt3jR07Vm63u9bbBgAAjGfYJSqXy6UjR47o+PHjoWXFxcXKzc0tt15WVpays7O1bt06bd26VX379tX06dMlSWfPntWwYcMUCAS0bt065eTkaNWqVSoqKtLw4cN19uzZWm0TAAAwB8MCjtPpVJ8+fZSTkxNa9s4776hHjx4VbnP27Fn985//VHR0tCRpy5YtCgQCeuKJJxQZGSlJioyM1JNPPqnCwkK9++67NdsIAABgSobegzNgwABNmjRJY8aMkSStW7dOU6ZM0dKlS0Pr3H///ZKkU6dOyeVyKTk5WX/84x8lSXv27NH1119/wX4dDoe6du2qTz/9VH369Knw+30+nzwez5Vskul4vV7bt9GMuFG47uE4sw7GReuprM8qGm8NDTgdO3aU0+nU/v371aRJExUVFalt27bl1snKylJMTIwOHDigUaNGqUuXLmrSpEno84ouQ5WWlsrpdFb6/S6Xy/Y/RB6Px/ZtBMyA48w6GBetpyp9Zvhj4v3799f69euVnZ2t1NTUCtfr0KGDnnjiCaWnpys/P1+S1LlzZ33yyScKBALl1g0EAtq9e7eSkpJqtHYAAGBOhgec1NRUbdmyRZs2bVJKSkql66akpCgxMTF0iapXr16KjIzUjBkz5PV6JX1/GuuZZ55RgwYNdOutt9Z4/QAAwHwMDzixsbFq3bq14uLi1KhRo4uun5GRoT//+c/6y1/+onr16mnp0qWqX7++7rjjDqWkpGjgwIGqX7++li5dqvDw8FpoAQAAMBtHMBgMGl2EUerCddi60Eaz4kV/dQcv+rMWxkXrqUqf8SZjoAZ4/WX86NUhRSU+NYh0GV0GgHMYfokKsCN3eOVP8FWGx1et59jRPKNLAHAeAg4AALAdAg4AALAdAg4AALAdAg4AALAdAg4AALAdAg4AALAdAg4AALAdAg4AALAdAg4AALAdAg5QQ7z+siptxxw51tMyrpXRJQA4D3NRATXEHe5kws06gnnHAPMxRcCJj4/Xzp07FRMTE1q2du1abd26VS+++KIkacmSJdqwYYOCwaACgYC6deumcePGyev1Ki0tTZJUXFysEydO6Oqrr5Yk3XTTTXr88cdrv0EAAMBQpgg4F7N582Zt27ZNK1eulNvtls/n0yOPPKIXXnhB48ePV3Z2tiTp448/1jPPPBP6GwAA1E2WCDgnT55UWVmZvF6v3G63XC6XMjIyVFBQYHRpAADAhEwTcO6//36Fhf3fPc+nT59WfHy8JGngwIH64IMPdPPNN6tDhw5KSkpSjx49dMMNNxhVLgAAMDHTBJysrKwfvQdHkqKiorR06VJ9+eWX+uijj7Rr1y6NGjVKQ4YM0aRJk6r8nT6fTx6Pp9q1m5nX67V9G82Kp6HqFo4z62BctJ7K+qyisdY0AacyS5Ys0XXXXafOnTurRYsWGjRokD755BONHDmyWgHH5XLZ/kfI4/HYvo2AGXCcWQfjovVUpc8s8R4cr9erOXPm6Ntvvw0tO3TokNq3b29gVQAAwKwscQbnoYceksPh0ODBg+VwOBQIBNSxY0fNnTvX6NIAAIAJOYLBYNDoIoxSF05T1oU2mhkv+qsbeNGftTAuWk9V+swSZ3AAK/L6y/jhqyOKSnxqEOkyugwA57DEPTiAFbnDnVXajqc7rOfY0TyjSwBwHgIOAACwHQIOAACwHQIOAACwHQIOAACwHQIOAACwHQIOAACwHQIOAACwHQIOAACwHQIOAACwHQIOUEu8/rJLWo85cqynZVwro0sAcB7mogJqiTvcyeSbNsWcY4D5mO4MTn5+vuLj43Xvvfde8Fl6erri4+NVUFCgvXv3Ki0tTf369VNKSopGjBihv//976F1u3fvrn379tVm6QAAwCRMeQbH5XLpyJEjOn78uJo1ayZJKi4uVm5uriQpEAho9OjRWrp0qTp06CBJys7O1siRI/Xee+/J6azaJIcAAMAeTHcGR5KcTqf69OmjnJyc0LJ33nlHPXr0kCSFhYXpzJkzKi4uDn3ev39/ZWRkqKzs0u5zAAAA9mXKgCNJAwYMUHZ2dujvdevWaeDAgaG/J02apBEjRqhHjx6aNGmS1qxZo5tuukkRERFGlAsAAEzElJeoJKljx45yOp3av3+/mjRpoqKiIrVt2zb0+bBhwzRo0CDt3r1bu3fv1pIlS7RkyRKtXr1aUVFRl/QdPp9PHo+npppgCl6v1/ZttAqejrI3jjPrYFy0nsr6rKKx1bQBR/r+stP69esVExOj1NTU0PIvvvhCn332mUaMGKHk5GQlJydr/PjxSklJ0YcffqjevXtf0v5dLpftf3Q8Ho/t2wiYAceZdTAuWk9V+sy0l6gkKTU1VVu2bNGmTZuUkpISWu52u7V48WJ98sknoWUnT55UYWFhubM8AACgbjL1GZzY2Fi1bt1aUVFRatSoUWh58+bNtXDhQj3//PP6+uuv5XK5FBUVpRkzZqhVK164BQBAXWe6gNO8eXPt2bMn9Perr75a7vODBw9Kkm688UbdeOONFe5n+/btNVMgAAAwPdMFHMCuvP4y3nhrU0UlPjWIdBldBoBzmPoeHMBO3OGX9gJKnu6wnmNH84wuAcB5CDgAAMB2CDgAAMB2CDgAAMB2CDgAAMB2CDgAAMB2CDgAAMB2CDgAAMB2CDgAAMB2CDgAAMB2CDiACXj9ZaF/JyQkGFgJqqJlHJP8AmbDXFSACbjDnYpL32h0Gagi5hgDzMcWZ3Dy8/OVlJRUbtmmTZvUpUsX7dy506CqAACAUWx5BufNN9/UokWLtGzZMk73AwBQB9ku4Lz00ktau3at3njjDTVv3tzocgAAgAFscYnqB7NmzdKcOXOUlpZGuAEAoA6zzRmc4uJiHTp0SC+99JLGjRunpKQktW/fvtJtfD6fPB5PLVVoDK/Xa/s22gGXUq2P48w6GBetp7I+q2j8tE3AcbvdWrx4scLDwzV69Gj9/ve/19q1a9WoUaMKt3G5XLb/YfF4PLZvI2AGHGfWwbhoPVXpM9tcogoLC1N4eLgkadSoUWrTpo0mTJigQCBgcGUAAKC22SbgnMvhcGjmzJk6fPiw5s6da3Q5AACgltniElXz5s21Z8+ecssaN26sDz74wJiCAACAoWwRcACr8/rLeBuuhRWV+NQg0mV0GQDOYctLVIDVuMOdoX/zdIf1HDuaZ3QJAM5DwAEAALZDwAEAALZDwAEAALZDwAEAALZDwAEAALZDwAEAALZDwAEAALZDwAEAALZDwAEAALZDwAFMwusvkyQlJCQYXAkuV8u4VkaXAOA8zEUFmIQ73Km49I1Gl4EqYB4xwHxMEXDKysr02muvKScnR2VlZfL7/UpOTtadd96p/v3767333lNsbGy5bfr166dHHnlEt956q5YsWaINGzYoGAwqEAioW7duGjdunCIiIgxqEQAAMJIpLlFlZmZqz549ysrKUnZ2tlavXq0jR45o8eLFuummm7R27dpy6+/Zs0dnzpxR9+7dtXnzZm3btk0rV67U+vXrtWbNGuXl5emFF14wqDUAAMBohp/Byc/PV05Ojnbs2KGGDRtKkurXr69p06YpNzdXbrdb06dP15gxY+RwOCRJq1at0uDBg+V0OnXy5EmVlZXJ6/XK7XbL5XIpIyNDBQUFRjYLAAAYyPCAc+DAAbVp0yYUbn7QtGlT9erVS4FAQMFgULt27VKXLl105swZvffee9q8ebMkaeDAgfrggw908803q0OHDkpKSlKPHj10ww03GNEcAABgAoYHnLCwMAUCgUo/Hzx4sNasWaMuXbpo/fr1uuWWW9SkSRNJUlRUlJYuXaovv/xSH330kXbt2qVRo0ZpyJAhmjRpUqXf7fP55PF4rmh7zMbr9dq+jXbB01PWxnFmHYyL1lNZn1U0dhoecBITE5WXl6fCwsJyZ3FOnDihjIwMzZ8/X3feead69+6twsJCrVq1StOmTQutt2TJEl133XXq3LmzWrRooUGDBumTTz7RyJEjLxpwXC6X7X9UPB6P7dsImAHHmXUwLlpPVfrM8JuMY2Nj1a9fP02ZMkWFhYWSpMLCQmVmZqpRo0Zyu91q3LixkpOTNX/+fDmdTl177bWh7b1er+bMmaNvv/02tOzQoUNq3759rbcFAACYg+FncCRp6tSpWrRoUejG4dLSUvXs2VMPP/xwaJ0hQ4borrvu0rPPPltu24ceekgOh0ODBw+Ww+FQIBBQx44dNXfu3NpuBgAAMAlHMBgMGl2EUerCacq60EY74UV/1sSL/qyFcdF6qtJnpjiDA+D7qRr4obSmohKfGkS6jC4DwDkMvwcHwPfc4U5JPI1jRceO5hldAoDzEHAAAIDtEHAAAIDtEHAAAIDtEHAAAIDtEHAAAIDtEHAAAIDtEHAAAIDtEHAAAIDtEHAAAIDtEHAAE/H6y5gjx4JaxrUyugQA58zRLJUAACAASURBVGEuKsBE3OFOJty0IOYQA8zHNAEnPj5ebdu2VVjY/51U6tixo5599lmlpaXp+PHjioqKkiQFAgGVlpZq7NixGjBggAYPHqySkhL5/X4dOXJEbdu2lSS1adNGc+bMMaQ9AADAOKYJOJKUlZWlmJiYH/1s8uTJ6t27d+jvffv26Z577lHPnj315ptvSpLy8/PVr18/ZWdn10q9AADAnCx7D86XX36p+vXrKyIiwuhSAACAyZjqDM79999f7hLV0qVL1aRJE0nSrFmztHjxYn333Xfy+Xy68cYbtWzZMgIOAAC4gKkCzqVcoiooKNDIkSMVGxur9u3bV+v7fD6fPB5PtfZhdl6v1/ZttBOeoLIujjPrYFy0nsr6rKJx01QB51LExMRo7ty5SklJUVJSkm677bYq78vlctn+B8Xj8di+jYAZcJxZB+Oi9VSlzyx5D06LFi00ZswYPfvssyouLja6HAAAYDKWDDiSNHz4cLndbi1evNjoUgAAgMmY5hLVwYMHK/xs+fLlFyyLiIjQ1q1byy1r3ry59uzZc8VrAwAA1mKagAPg+6kaeCuu9RSV+NQg0mV0GQDOYdlLVIAducOdPN1hQceO5hldAoDzEHAAAIDtEHAAAIDtEHAAAIDtEHAAAIDtEHAAAIDtEHAAAIDtEHAAAIDtEHAAAIDtEHAAAIDtEHAAoJpaxrUyugRchoSEhAo/8/rLarES1CTmogKAamoQ6VJc+kajy8AVwFxw9lGjZ3D8fr9uvvlmjRgxIrQsPz9f8fHxuvfeey9YPz09XfHx8SooKAgtW716tQYNGqS+ffuqZ8+eGjZsmP7617+GPk9LS1NaWpoCgUBoWUFBgeLj42uoVQAAwOxqNOC8++67ateunfbv36/Dhw+HlrtcLh05ckTHjx8PLSsuLlZubm657Z977jmtWbNGc+fO1aZNm7Rt2zaNGjVKo0eP1ldffRVab+/evfrv//7vmmwKAACwkBoNOCtWrFCPHj3Ut29fZWVlhZY7nU716dNHOTk5oWXvvPOOevToEfr73//+t7KysjRv3jw1a9YstLxr165KT09XSUlJaNlDDz2kpUuXau/evTXZHAAAYBE1FnC++OIL7dmzR71799aAAQOUnZ2tU6dOhT7/YdkP1q1bp4EDB4b+3rt3r1q3bq2f/exnF+x7wIABat26dejvq6++WpMnT9bEiRNVWFhYQy0CAABWUWM3Ga9YsULJyclq3LixGjdurObNm2vVqlW6/fbvb+Dq2LGjnE6n9u/fryZNmqioqEht27YNbR8MBsvtr7CwUEOHDpX0/eWsPn36aPz48aHP77rrLu3YsUOZmZmaMmXKJdXo8/nk8Xiq21RT83q9tm+j3dBn1lPZUzmwHo4/86lsXKzo+KuRgFNcXKzs7GxFRESoe/fukr4PKK+//rp69eoVWq9///5av369YmJilJqaWm4fiYmJOnLkiE6dOqXGjRurYcOGoTM+CxYsKHc26AfPPPNMaJ+XwuVy2X5g8ng8tm+j3dBngLE4/synKuNijQScnJwcNWrUSFu3bpXT6ZQkfffdd0pOTtaWLVtC66WmpmrQoEFq1KiRXnvttXL7iI2N1X333adHH31U//Vf/6WrrrpKknT8+HHl5uaWu0T1g+joaM2ePVsjR46siWYBAACLqJGAs2LFCg0bNiwUbiTpJz/5idLS0rRs2bLQstjYWLVu3VpRUVFq1KjRBfsZN26c1q9frwkTJqikpERnzpxRdHS0+vbtG7pcdb5f/epXeuCBB3iqCgCAOswRPP9mlzqkLlwKqAtttBv6zJp40Z898KI/czLNJSoAqEuKSnz8MNqE118md7jz4ivC9JiLCgCq6djRPKNLwGWo7Ckpwo19EHAAAIDtEHAAAIDtEHAAAIDtEHAAAIDtEHAAAIDtEHAAAIDtEHAAAIDtEHAAAIDtEHAAAIDtEHAAoJpaxrUyugRchovNaeT1l9VSJahJzEUFANXUINLFZJs2wrxi9mBowMnPz9ett96qtm3bSpICgYAaNGig++67T3379pUkFRQU6LnnntPHH3+syMhIhYWFKSUlRcOGDZPT6VRaWpq6deumUaNGldv30qVLtXv3bi1evLjW2wUAAIxl+CUqt9ut7OxsZWdnKycnR3PmzNHzzz+vrVu36rvvvtM999yjuLg4bd68WevXr1dWVpb27dunyZMnS5KGDBmiNWvWXLDfVatWaejQobXdHAAAYAKGB5zzNWvWTI888oheeeUVrVixQgkJCRoxYoTq1fv+ZFN0dLRmzZqlnTt36rPPPtOtt96q4uJiffLJJ6F97Nq1S8FgUP/5n/9pVDMAAICBTBdwJKldu3Y6dOiQ9uzZoxtuuOGCz10ul6677jrl5uaqXr16uuuuu7R69erQ5ytXrtSQIUPkcDhqs2wAAGASprzJ2OFwyO12S5L8fv+PrlNaWhr691133aXbb79dhYWFOnv2rHbs2KHMzMyLfo/P55PH47kiNZuV1+u1fRvthj6znos9lQPr4Rg0l8rGxYqOP1MGnH379qlt27bq3Lmzdu3apQceeKDc50VFRdq3b59+97vfSZJiY2N10003adOmTSouLlavXr0UFRV10e9xuVy2H5g8Ho/t22g39BlgPI5Bc6nKuGi6S1RHjhzRokWL9OCDD2rIkCE6fPiwXnrpJZWVff9egtOnTys9PV3XX3+9EhMTQ9sNHTpUOTk5WrduHTcXAwBQxxl+Bsfr9So1NVWSFBYWJpfLpfHjx+s3v/mNpO/vp5k3b5769u2r8PBwORwOpaSk6MEHHyy3ny5dumj69OmKjo5WfHx8bTcDAACYiKEBp3nz5he9ztmoUSNNnTr1kvaXk5NzJcoCAAAWZ/gZHACwuqISH2+/tRGvv0zucKfRZaCaTHcPDgBYzbGjeUaXgMtwsSsHhBt7IOAAAADbIeAAAADbIeAAAADbIeAAAADbuWjACQaDtVEHAADAFXPRgDN8+PDaqAMAAOCKueh7cKKiorRt2zZdffXVCgv7Pg9dffXVNV4YAABAVV004BQUFCgrKyv0t8Ph0GuvvVajRQEAAFTHRQPO8uXLdebMGR0/flwtWrRQgwYNaqMuAACAKrtowNm6dasWL16ssrIy9e7dWw6HQw899FBt1AYAltAyrpXRJeAyJCQkXNJ6TNlgbRcNOK+++qpWrVql4cOH66GHHtKdd95JwAGAczSIdCkufaPRZeAKY34xa7voU1RhYWGKiIiQw+GQw+FQZGRkbdT1o+Lj41VQUKCysjK9+uqruuOOO5Samqq+fftq9uzZKi0tlSR9/PHHSklJMaxOAABgrIsGnOuvv14TJkzQiRMn9PTTT6tTp061UVelMjMztWfPHmVlZSk7O1urV6/WkSNH9OSTTxpdGgAAMIGLXqIaP368/vd//1cJCQlq1aqVunfvXht1Vej48ePKycnRjh071LBhQ0lS/fr1NW3aNOXm5hpaGwAAMIeLnsHZsGGDfv3rX2vEiBHq2LGjRowYURt1VejLL79UmzZtQuHmB02bNlWvXr0MqgoAAJjJRc/grFu3Tg0aNFBpaamee+45PfLII7VRV4UcDocCgcAV2ZfP55PH47ki+zIrr9dr+zbaDX1mPZf6VA6sh2PRHCobFys6/i4acF544QWNGTNGPp9PK1asUExMTPWqvAx/+9vf5HQ6FR8fH5oTKzExUXl5eSosLCx3FufEiRPKyMjQ/PnzL3n/LpfL9gOTx+OxfRvthj4DzINj0RyqMi5WGHDGjx8vh8MhSXK73frss8/07LPPSpLmzJlTjTIv3fvvv6+jR49q9uzZOnDggGJiYnTVVVepX79+mjJlimbMmKGGDRuqsLBQmZmZatSokdxud63UBgAAzKvCgDN48OByfz/44IM1Xsz57r33Xk2YMEEpKSny+/2aPn26HA6Hpk6dqkWLFmnw4MFyOp0qLS1Vz5499fDDD9d6jQAAwHwqDDi/+tWvJEnbt2/Xvn379Oijj2r48OF64IEHaqs2RUdH6+WXX75geb169fTII49UeD9Qly5dtGHDhpouDwAAmNRF78FZsGBBKGTMnTtXI0eOVLdu3Wq8MACwiqISH2+9tSGmarC2iz4mXq9ePTVp0kSSFBUVpbCwi24CAHXKsaN5RpeAy3CpT0YRbqztomdwEhMTNWHCBF177bX67LPP1L59+9qoCwAAoMouGnCeeuopvffee8rLy1OfPn0Mf5MxAADAxVR4ven999+XJK1atUrffPONoqOjdfLkSa1cubLWigMAAKiKCgPO6dOnJX0/seXJkydD/+Xn59dacQAAAFVR4SUqv9+vu+++W/Xr19df/vIXSVIgENDZs2c1YcKEWisQAADgclUYcFJTU9W1a1e9+OKLGjNmjCQpLCws9EQVAACAWVUYcCIiItS8eXM988wztVkPAABAtfFSGwAAYDsEHAAAYDsEHACoppZxrYwuAZchISGh2vvw+suuQCWoSRd90R8AoHINIl2KS99odBmoRcw9Zn6mCDgrVqzQihUrdPbsWTkcDrVv317jxo3TVVddpbS0NA0dOlS9e/eWJJ04cULDhg1T165d9eSTT2rKlCn68MMPFRMTU26fd955p+677z4jmgMAAAxmeMCZOXOmPv/8c7344ov6xS9+oUAgoPXr1+vuu+/WW2+9VW7df/zjHxo2bJjuvvtujR49OrT8gQce0PDhw2u7dAAAYFKGBpyvv/5ab775pj744ANFR0dL+v5dOwMGDND+/fv14osvhtb9/PPPNXr0aI0bN04DBgwwqmQAAGABhgacv/71r2rVqlUo3Jzrpptu0ty5cxUdHa3c3FxlZGSoVatW6t+//wXrLlu2TOvXry+3bNasWYqPj6+x2gEAgHkZfonq7NmzP7q8tLRUDodDkrR+/XotXLhQ06dP1/PPP3/BVBFVvUTl8/nk8Xguv2gL8Xq9tm+j3dBn1nMlnsqB9XCc1p7KxsWKjj9DA861116rf/zjHzp58qSaNm1a7rOPP/5YSUlJOnz4sKZMmaJf/epXmjdvnn7729+qU6dOuu2226r9/S6Xy/YDk8fjsX0b7YY+A6yB47T2VGVcNPQ9OLGxsUpLS9P48eN14sSJ0PI1a9bonXfe0ciRIyV9P22EJF199dV65plnlJ6ersOHDxtSMwAAMD/DL1FNmDBBb731lsaOHavS0lKVlpaqU6dOevPNN9WsWbML1u/bt692796t3/3ud1q9erWkH78H55prrtEf/vCHWmkDAAAwF0cwGAwaXYRR6sKlgLrQRruhz6yJF/3VLbzor3ZVZVw0/AwOAFhdUYmPH7w6xusvkzvcaXQZqARzUQFANR07mmd0CbgMV+LpJ8KN+RFwAACA7RBwAACA7RBwAACA7RBwAACA7RBwAACA7RBwAACA7RBwAACA7RBwAACA7RBwAACA7RBwAKCaWsa1MroEXIaamuvN6y+rkf2iapiLCgCqqUGki8k2wXxkJmP4GZz4+HgVFBSUW7ZlyxalpaVJktauXavExEQdOnSo3DqjR4/W2rVrJUlpaWnq3r27UlNTNWDAAN1+++16/PHHVVJSUjuNAAAApmJ4wLkUwWBQEyZMkM/nq3CdyZMnKzs7W+vWrdOGDRtUUlKi+fPn12KVAADALCwRcLp27aqf/vSnmjlz5iWt73A41KVLF+XlMcMvAAB1kSUCjsPh0MyZM7V582a9//77F13/9OnT2rx5s7p06VIL1QEAALMx/CZjh8NxwbJAIKCwsPLZ62c/+5meffZZTZkyRevXr79gm1mzZmnx4sUKBoOSpOTkZN13332VfrfP55PH46lG9ebn9Xpt30a7oc+sp6aeyoH1cOzWjMrGxYqOP8MDTuPGjfXtt98qJiYmtOybb75Ro0aNLli3e/fu6t27tx5//HHVq1e+9MmTJ6t3796X9d0ul8v2A5PH47F9G+2GPgOsi2O3ZlRlXDT8EtWvf/1rLV++XIFAQNL3l5fefvtt3XLLLT+6fnp6uv71r39p586dtVkmAACwEMMDzpNPPimfz6eUlBT169dP9957r/r27auBAwf+6Poul0tz5sz50UtbAAAAkgkuUf3kJz/RjBkzKvz8jjvu0B133FFuWXx8vD777LPQ38uXL6+x+gAAgPUYHnAAwOqKSny8xRby+svkDncaXQb+f4ZfogIAqzt2lHduWUlNPelEuDEXAg4AALAdAg4AALAdAg4AALAdAg4AALAdAg4AALAdAg4AALAdAg4AALAdAg4AALAdAg4AALAdAg4AVFPLuFZGl4DLkJCQUCvf4/WX1cr34McxFxUAVFODSJfi0jcaXQZMhvnJjGX5gJOfn69bb71Vbdu2lSQFAgE1aNBA9913n/r27WtwdQAAwAiWDziS5Ha7lZ2dHfr7+PHjeuCBB+R0OtWrVy8DKwMAAEaw5T04zZo10yOPPKJXXnnF6FIAAIABbBlwJKldu3Y6dOiQ0WUAAAAD2OIS1Y9xOBxyu92VruPz+eTxeGqpImN4vV7bt9Fu6DPrqa2ncmA9HMtXRmXjYkXHn20Dzr59+0I3HlfE5XLZfmDyeDy2b6Pd0GeAfXAsXxlVGRdteYnqyJEjWrRokR588EGjSwEAAAawxRkcr9er1NRUSVJYWJhcLpfGjx+v3/zmN8YWBgAADGH5gNO8eXOucQIAgHIsH3AAwGhFJT7eWosLeP1lcoc7jS6jzrLlPTgAUJuOHc0zugRchto660+4MRYBBwAA2A4BBwAA2A4BBwAA2A4BBwAA2A4BBwAA2A4BBwAA2A4BBwAA2A4BBwAA2A4BBwAA2A4BBwCqqWVcK6NLwGVISEio1e/z+stq9fvwPeaiAoBqahDpUlz6RqPLgEkxT5kxTHUGp6ysTK+++qruuOMOpaamqm/fvpo9e7ZKS0u1YMEC/eEPf7hgmzNnzui2227T8uXLQ8uCwaDGjBmjP/3pT7VZPgAAMAlTncHJzMzU6dOnlZWVpaioKBUXF2vixIl68skn1bJlyx/dJioqSvPnz9fQoUN1zTXXKDExUfPmzZPf79f48eNruQUAAMAMTBNw8vPzlZOTox07dqhhw4aSpPr162vatGnKzc3VoUOHKty2Xbt2Sk9P12OPPaZHH31UGzdu1OrVqxUWZqoTVAAAoJaYJgEcOHBAbdq0CYWbHzRt2lS9evW66PaDBg1SUlKS0tPTtWDBAkVHR9dUqQAAwORMcwYnLCxMgUCgytufOXNG+/fvV5MmTbR9+3a1a9fuotv4fD55PJ4qf6cVeL1e27fRbugz66ntp3JgPRzT1VPZuFjR8WeagJOYmKi8vDwVFhaWO4tz4sQJZWRk6Je//GWF2waDQU2aNEldunRRWlqa7r77biUlJalr166VfqfL5bL9wOTxeGzfRruhzwD74ZiunqqMi6a5RBUbG6t+/fppypQpKiwslCQVFhYqMzNTjRo1ktvtrnDb+fPn61//+peeeuop/fKXv1RGRoYmTJigEydO1Fb5AADAREwTcCRp6tSpatOmjQYPHqzU1FQNGjRIbdq00fTp0yVJq1atUlJSUui/wYMHa9u2bXrjjTc0f/58RURESJIGDhyo3/zmN3rsscd09uxZI5sEAAAM4AgGg0GjizBKXbgUUBfaaDf0mTXxoj9UhBf9VV9VxkXT3IMDAFZVVOLjRwwV8vrL5A53Gl1GnWOqS1QAYEXHjuYZXQIuQ20/0US4MQYBBwAA2A4BBwAA2A4BBwAA2A4BBwAA2A4BBwAA2A4BBwAA2A4BBwAA2A4BBwAA2A4BBwAA2A4BBwCqqWVcK6NLwGUww1xvXn+Z0SXYHnNRAUA1NYh0MdkmLgtzl9U80wac+Ph4tW3bVmFh5U8yLVy4UM2bN1f37t01b948xcXF6c4771RaWprS0tIkScFgUGPHjlWbNm00ceJEI8oHAAAGMm3AkaSsrCzFxMRUuk5UVJTmz5+voUOH6pprrlFiYqLmzZsnv9+v8ePH11KlAADATGxxD067du2Unp6uxx57TNnZ2dq4caOee+65C87+AACAusHUZ3Duv//+ciGlefPmWrhw4Y+uO2jQIH300UdKT0/X22+/rejo6NoqEwAAmIypA86lXKL6wZkzZ7R//341adJE27dvV7t27S66jc/nk8fjqW6Zpub1em3fRruhz6zHDE/lwHo4zi9dZeNiRcefqQPOpQoGg5o0aZK6dOmitLQ03X333UpKSlLXrl0r3c7lctl+YPJ4PLZvo93QZ0DdwHF+6aoyLtriJpX58+frX//6l5566in98pe/VEZGhiZMmKATJ04YXRoAADCAqc/gnH8PjiSNHz9et9xyS+jvbdu26Y033tCaNWsUEREhSRo4cKB2796txx57TMuXL1e9eqZuJgAAuMJM+8t/8ODBSj/fvn27JKlTp07q2bPnBZ/PmDGjRuoCAADmZ9qAAwBWUVTi4820uCxef5nc4U6jy7A1W9yDAwBGOnY0z+gScBnM8PQS4abmEXAAAIDtEHAAAIDtEHAAAIDtEHAAAIDtEHAAAIDtEHAAAIDtEHAAAIDtEHAAAIDtEHAAAIDtEHAAoJpaxrUyugRchoSEBKNLkPT9dA2oOcxFBQDV1CDSpbj0jUaXAYth/rKaZXjAiY+PV9u2bRUWFiaHw6GSkhI1bNhQmZmZ6tSpkySpuLhYCxYs0Pbt2xURESFJ6t69u8aOHSu32x3az86dOxUTE2NYWwAAgDmY4hJVVlaWsrOztW7dOm3dulV9+/bV9OnTJUlnz57VsGHDFAgEtG7dOuXk5GjVqlUqKirS8OHDdfbsWYOrBwAAZmOKgHOus2fP6p///Keio6MlSVu2bFEgENATTzyhyMhISVJkZKSefPJJFRYW6t133zWyXAAAYEKGX6KSpPvvv1+SdOrUKblcLiUnJ+uPf/yjJGnPnj26/vrrL9jG4XCoa9eu+vTTT9WnT59arRcAAJibKQJOVlaWYmJidODAAY0aNUpdunRRkyZNQp9XdBmqtLRUTqezyt/r8/nk8XiqvL0VeL1e27fRbugz6zHLUzmwHo71S1PZuFjR8WeKgPODDh066IknnlB6eroSEhLUvHlzde7cWS+//LICgYDCwv7vilogENDu3bs1duzYKn+fy+Wy/cDk8Xhs30a7oc+AuoNj/dJUZVw03T04KSkpSkxMDF2i6tWrlyIjIzVjxgx5vV5J3ye5Z555Rg0aNNCtt95qZLkAAMCETBdwJCkjI0N//vOf9Ze//EX16tXT0qVLVb9+fd1xxx1KSUnRwIEDVb9+fS1dulTh4eGh7Xr06KGkpKTQf++//76BrQAAAEYx/BLVwYMHL1jWqlUr7d+/P/S32+3W+PHjNX78+MvaDwAAqJsMDzgAYHVFJT7eSovL5vWXyR1e9QdlUDlTXqICACs5djTP6BJwGczy5BLhpmYRcAAAgO0QcAAAgO0QcAAAgO0QcAAAgO0QcAAAgO0QcAAAgO0QcAAAgO0QcAAAgO0QcAAAgO0QcACgmlrGtTK6BFyGhIQEo0u4gNdfZnQJtsNcVABQTQ0iXYpL32h0GbAw5jK78kwbcFavXq2VK1eqqKhIpaWlatGihR577DFdc801WrBggU6dOqWnn35akrRkyRJt2LBBwWBQgUBA3bp107hx4xQREWFwKwAAgBFMGXCee+457d69W3PnzlWzZs0kSTt37tTo0aO1du3acutu3rxZ27Zt08qVK+V2u+Xz+fTII4/ohRde0Pjx440oHwAAGMx0Aeff//63srKy9O677+pnP/tZaHnXrl2Vnp6ukpKScuufPHlSZWVl8nq9crvdcrlcysjIUEFBQW2XDgAATMJ0AWfv3r1q3bp1uXDzgwEDBlywbODAgfrggw908803q0OHDkpKSlKPHj10ww031Ea5AADAhEwXcILBYLm/CwsLNXToUElScXGx+vTpo/Dw8NDnUVFRWrp0qb788kt99NFH2rVrl0aNGqUhQ4Zo0qRJlX6Xz+eTx+O58o0wEa/Xa/s22g19Zj1mfCoH1sNxX7HKxsWKjj/TBZzExEQdOXJEp06dUuPGjdWwYUNlZ2dLUujm4saNG4fWX7Jkia677jp17txZLVq00KBBg/TJJ59o5MiRFw04LpfL9gOTx+OxfRvthj4D6iaO+4pVZVw03XtwYmNjdd999+nRRx/VV199FVp+/Phx5ebmKiysfMler1dz5szRt99+G1p26NAhtW/fvtZqBgAA5mK6MziSNG7cOK1fv14TJkxQSUmJzpw5o+joaPXt21dDhw7Vyy+/HFr3oYceksPh0ODBg+VwOBQIBNSxY0fNnTvXwBYAAAAjOYLn3/RSh9SFSwF1oY12Q59ZEy/6Q3Xwor/KVWVcNOUZHACwkqISHz9QqBavv0zucKfRZdiK6e7BAQCrOXY0z+gScBnM+LQS4ebKI+AAAADbIeAAAADbIeAAAADbIeAAAADbIeAAAADbIeAAAADbIeAAAADbIeAAAADbIeAAAADbIeAAQDW1jGtldAm4DFae683rLzO6BMtgLioAqKYGkS4m20StYM6zS8cZHAAAYDuGn8EpKyvTa6+9ppycHJWVlcnv9ys5OVmPPvqoIiIiVFBQoOeee04ff/yxIiMjFRYWppSUFA0bNkxOp1P5+fm69dZb1bZt29A+g8Gg7rvvPv32t781sGUAAMAohgeczMxMnT59WllZWYqKilJxcbEmTpyoJ598UhkZGbrnnns0aNAgZWZmql69ejp9+rSefvppTZ48WXPmzJEkud1uZWdnh/Z54sQJpaSkqGPHjmrXrp1RTQMAAAYxNODk5+crJydHO3bsUMOGDSVJ9evX17Rp05Sbm6sVK1YoISFBI0aMCG0THR2tWbNmKTk5WZ999pliYmIu2G9sbKz+4z/+Q0ePHiXgox11AwAAGBtJREFUAABQBxkacA4cOKA2bdqEws0PmjZtql69emnMmDHq1q3bBdu5XC5dd911ys3NVc+ePS/4fM+ePTp27JiuueaaSr/f5/PJ4/FUrxEm5/V6bd9Gu6HPrMfKT+XAeuri+FDZuFjR8WdowAkLC1MgEKh0Hb/f/6PLS0tLQ//2er1KTU2V9P09PY0bN9bs2bP1i1/8otJ9u1wu2w9MHo/H9m20G/oMQGXq4vhQlXHR0ICTmJiovLw8FRYWljuLc+LECWVkZOi6667Trl279MADD5TbrqioSPv27dPvfvc7SRfegwMAAOo2Qx8Tj42NVb9+/TRlyhQVFhZKkgoLC5WZmalGjRpp6NChOnz4sF566SWVlX3/cqPTp08rPT1d119/vRITE40sHwAAmJThT1FNnTpVixYt0uDBg+V0OlVaWqqePXvq4f+vvXsPiuo83Dj+LKsuDHgjsYoaRKzgxDgqtbWxyEXjEC+j2OiYzsR7vGR6i1oq6YyXzCRqR5NYbWqpTqo1FgzqBKwZg/USTYt4b4tZzaSKxF4YG5tWkOW6vz+c7K9GBUXlPfvu9/PfHnYPzztn9uXxPed4vv99tWvXTtu3b9fPfvYzjRkzRm3btpXL5dK4ceM0a9Ys09EBAIBDufx+v990CFNC4VqHUBijbThmwaequkaRER7TMRACfHUNCm/rNh2j1bVkXuR/MgaA+1RedsF0BNyDYL4LKRTLTUtRcAAAgHUoOAAAwDoUHAAAYB0KDgAAsA4FBwAAWIeCAwAArEPBAQAA1qHgAAAA61BwAACAdSg4AHCfYuPiTUfAPbD1USi+ugbTERzF+MM2ASDYRUZ4FJe9x3QMhLiyVWNNR3AUVnAAAIB1HLWCU1dXp/T0dPXr10+bNm0KbE9MTFRCQoLCwm7uY2+++aYkadSoUUpISAhs9/v9mjZtmiZNmtQ6wQEAgKM4quDs27dP/fr1U2lpqf7617+qT58+gZ9t2bJF0dHRt3zm8uXLCg8PV0FBQWBbRUWFxo0bpyeeeEL9+vVrlewAAMA5HHWKKjc3VyNHjtSYMWO0ZcuWFu+na9eu6tWrl8rKyh5cOAAAEDQcs4LzySef6PTp01q3bp369++vqVOnasGCBercubMkafr06TedourZs2fgFNWXnT59WuXl5Ro4cGCTv7OmpkZer/fBDcKBfD6f9WO0Dccs+Nh6Vw6Cj61zR1Pz4p2+f44pOLm5uUpPT1fnzp3VuXNn9ezZU++8847mzZsn6c6nqKQbA58wYYIkqaGhQZ07d9bq1asVExPT5O/0eDzWT0xer9f6MdqGYwagpWydO1oyLzqi4Fy/fl0FBQVq166dRowYIUmqrKzU22+/rVmzZjX7+S9fgwMAAEKbIwrO7t271alTJ73//vtyu92SpP/+979KT0/X3r17DacDAADBxhEFJzc3VzNnzgyUG0nq0KGDpk6dqs2bN0u69RocSVq4cOFNd1oBAABIksvv9/tNhzAlFK51CIUx2oZjFnyqqmsUGeExHQMhzlfXoPC27ubfGIRaMi866jZxAAhG5WUXTEfAPbD1TiNby01LUXAAAIB1KDgAAMA6FBwAAGAdCg4AALAOBQcAAFiHggMAAKxDwQEAANah4AAAAOtQcAAAgHUoOABwn2Lj4k1HwD0IhUeh+OoaTEcwzhEP2wSAYBYZ4VFc9h7TMYCAslVjTUcwjhUcAABgHUes4Fy+fFmjRo1SQkJCYJvf79e0adM0adIkHTp0SBs2bFB1dbUaGhr01a9+VS+99JK6desWeP/Vq1eVlpamiRMn6uWXXzYxDAAA4BCOKDiSFB4eroKCgsDriooKjRs3Tr169dLixYu1a9cu9ejRQ5K0YcMGvfjii8rLywu8f8eOHRo5cqR+97vfacGCBerUqVOrjwEAADiDY09Rde3aVb169VJJSYnq6up0/fr1wM+mT5+uefPmBV43NjZq+/btmjhxooYMGaJ33nnHRGQAAOAQjlnB+bLTp0+rvLxczzzzjCorKzVx4kTFxsYqKSlJTz75pDIyMgLvPXLkiHw+n4YNG6aqqiqtXLlSs2bNUps2TQ+vpqZGXq/3YQ/FKJ/PZ/0YbcMxCz6hcFcOgo9N80hT8+Kdvn8uv9/vf5ih7saXr8FpaGhQ586d9fzzzys1NVWS9O9//1vHjh3T8ePHtW/fPsXExGjbtm1yu92aP3++4uLilJ2drdraWiUnJ2vp0qUaN25ck7/X6/VaPzGFwhhtwzELTtxFBSex7S6qlsyLjlnB+fI1OF/Yv3+/Pv/8cz3zzDPKyMhQRkaGFixYoNTUVH300UeKjo7WBx98oLNnz6qoqEiSVF9fr82bNzdbcAAAgJ0cew3OFyIjI/X666/rk08+CWz79NNP5Xa7FRsbq+3bt+trX/uajhw5ogMHDujAgQPatWuXPvroI506dcpgcgAAYIpjVnDu5Jvf/KaWLFmixYsX69q1a3K73erSpYs2btyoiIgI7dixQytWrLjpM3FxcRo7dqw2b96spKQkQ8kBAIApjrgGx5RQuNYhFMZoG45Z8KmqrlFkhMd0DCDAV9eg8LZu0zEemJbMi44/RQUATldedsF0BNwDm+4uuhObyk1LUXAAAIB1KDgAAMA6FBwAAGAdCg4AALAOBQcAAFiHggMAAKxDwQEAANah4AAAAOtQcAAAgHUoOABwn2Lj4k1HwD0I1Ueh+OoaTEdoVY5/2CYAOF1khEdx2XtMxwCaVLZqrOkIrYoVHAAAYB1HreCMGDFC3/72t7Vv3z5J0j/+8Q95PB5FR0dLkpYsWaLvfve7Ki4uVljYjW62cOFCFRUV6ejRo4qKipIkLV++XJGRkcrKyjIzEAAAYJTjVnBSU1NVUFCggoICjRgxQjNmzAi8TkpKkiSdP39eklRfX6+SkhINHTpUR44cCezj6NGjSktLMxEfAAA4gOMKTlPCwsKUnJyskpISSdLJkyeVmJiop59+WgcOHJAkVVRU6LPPPtPgwYNNRgUAAAY56hTV3Rg+fLiKioo0Y8YMHTx4UGlpaUpNTdWaNWvU0NCg4uJiJScnq02b5odWU1Mjr9fbCqnN8fl81o/RNhyz4BOqd+Ug+ATr3NLUvHin71/QFZyUlBStXLlSjY2NOnjwoDZt2qSvfOUr6tGjh0pLS3X06FGlpqbe1b48Ho/1E5PX67V+jLbhmAF4WIJ1bmnJvBhUp6gkKTo6Wj179lRRUZHcbrcee+wxSVJaWppOnjypY8eOKSUlxXBKAABgUtAVHOnGKs4vfvGLmy4kTktLU0FBgbp06RK46woAAISmoC0458+fV3p6emDbgAED9K9//YvVGwAAIJff7/ebDmFKKFzrEApjtA3HLPhUVdcoMsJjOgbQJF9dg8Lbuk3HaJGQuAYHAJymvOyC6Qi4B8F6J9H9CtZy01IUHAAAYB0KDgAAsA4FBwAAWIeCAwAArEPBAQAA1qHgAAAA61BwAACAdSg4AADAOhQcAABgHQoOANyn2Lh40xFwD3gUyt3z1TWYjtBibUwHAIBgFxnhUVz2HtMxgAeubNVY0xFajBUcAABgHccWnMuXLysxMVHPPffcLT/Lzs5WYmKirl69KknKzc3V+PHjNWbMGI0dO1ZZWVn6+9//3tqRAQCAQzj6FJXH49HFixf1t7/9TT169JAkXb9+XadOnQq856c//anOnTunnJwcxcTEqLGxUYWFhZoyZYry8/PVrVs3U/EBAIAhjl3BkSS3263Ro0dr9+7dgW1FRUUaOXKkJKm2tlZ5eXlau3atYmJiJElhYWHKzMxURkaGcnJyjOQGAABmOXoFR5IyMzOVlZWl+fPnS5Leffdd/eQnP9Fbb72lU6dOKT4+Xh07drzlc8OGDdPatWub3HdNTY28Xu9Dye0UPp/P+jHahmMWfLgrBzZzwnzU1Lx4p++f4wvOE088IbfbrdLSUj3yyCOqqqpSQkJC4Of19fW3/Vxtba1cLleT+/Z4PNZPTF6v1/ox2oZjBsBJnDAftWRedHzBkaTx48ersLBQ0dHRmjBhQmD7wIEDdenSJV25ckVdunS56TMlJSUaPHhwa0cFAAAO4OhrcL4wYcIE7d27V++9957GjRsX2B4REaGpU6dq4cKFqqioCGzfuXOnioqKNGfOHBNxAQCAYUGxgtO1a1f16dNH7du3V6dOnW762aJFi5Sfn68XXnhBtbW1qq2t1YABA5SXlxe48woAAIQWl9/v95sOYUooXOsQCmO0Dccs+FRV1ygywmM6BvDA+eoaFN7WbTpGi+bFoDhFBQBOVl52wXQE3AMn3BUULJxQblqKggMAAKxDwQEAANah4AAAAOtQcAAAgHUoOAAAwDoUHAAAYB0KDgAAsA4FBwAAWIeCAwAArEPBAYD7FBsXbzoC7gGPQrl/vroG0xGaFRQP2wQAJ4uM8Cgue4/pGECrKVs11nSEZrGCAwAArOP4FZzExEQVFxcrOjo6sG3Xrl16//33lZOTo/Xr12vbtm3q2rWrJKm+vl6JiYn6wQ9+oLi4OEOpAQCASY4vOHdjzJgxWrp0aeD1u+++q+nTp2vPnj2KiooymAwAAJhg5SmqzMxM9enTR7t37zYdBQAAGBAUKzjTp09XWNj/d7H//Oc/SkxMbPIziYmJ+vjjj5t8T01Njbxe7wPJ6FQ+n8/6MdqGYxZ8uCsHoag156mm5sU7ff+CouBs2bLlttfgNMXlcik8PLzJ93g8HusnJq/Xa/0YbcMxAxAMWnOeasm8aOUpKkn6y1/+0uwqDwAAsJOVBSc/P1+XL1/W6NGjTUcBAAAGBMUpqua89957OnnypFwulxobG9W7d2/95je/kcfjMR0NAAAY4PL7/X7TIUwJhWsdQmGMtuGYBZ+q6hpFRvAPKoQOX12Dwtu6W+33cQ0OABhQXnbBdATcA+5SvH+tWW5aioIDAACsQ8EBAADWoeAAAADrUHAAAIB1KDgAAMA6FBwAAGAdCg4AALAOBQcAAFiHggMAAKxDwQGA+xQbF286Au4Bj0J5sHx1DaYj3JYVD9sEAJMiIzyKy95jOgZgRNmqsaYj3BYrOAAAwDqOX8E5c+aMXnvtNX3++efy+/3q1q2bFi9erL59+0qScnNzlZubq/r6erlcLj3++ONasGCBunfvbjg5AAAwxdEFp7a2VvPmzdNbb72l/v37S5IKCgo0Z84c7d+/X2vWrNG5c+eUk5OjmJgYNTY2qrCwUFOmTFF+fr66detmeAQAAMAERxec6upqXbt2TdevXw9sGz9+vKKiolRRUaG8vDwdOnRIHTt2lCSFhYUpMzNTpaWlysnJ0bJly0xFBwAABjm64HTs2FFZWVl6/vnn9eijjyopKUlDhw7V2LFjdfjwYcXHxwfKzf8aNmyY1q5d2+z+a2pq5PV6H0Z0x/D5fNaP0TYcs+DDXTkIdQ97zmpqXrzT98/RBUeSZs6cqcmTJ+v48eM6fvy4Nm7cqI0bN2r+/Pmqr6+/7Wdqa2vlcrma3bfH47F+YvJ6vdaP0TYcMwDB5mHPWS2ZFx19F9XJkye1adMmRUVFKT09XT/+8Y+1Z8+eQHm5dOmSrly5csvnSkpKNHjw4NaOCwAAHMLRBSc6OlobNmzQiRMnAtuuXLmiyspKDRw4UFOnTtXChQtVUVER+PnOnTtVVFSkOXPmmIgMAAAcwNGnqHr37q0333xTb7zxhv75z3/K4/Goffv2WrFiheLj47Vo0SLl5+frhRdeUG1trWprazVgwADl5eWpR48epuMDAABDXH6/3286hCmhcK1DKIzRNhyz4FNVXaPICI/pGIARvroGhbd1P9TfYd01OAAQDMrLLpiOgHvAXYoP1sMuNy1FwQEAANah4AAAAOtQcAAAgHUoOAAAwDoUHAAAYB0KDgAAsA4FBwAAWIeCAwAArEPBAQAA1qHgAMB9io2LNx0B94BHobQ+X11Dq/9ORz9sEwCCQWSER3HZe0zHAByrbNXYVv+drOAAAADrGFnBmT17tlJSUjR9+nRJ0sWLF/X0009r3rx5WrhwoSTps88+U2pqqlJTU/XnP/9Z0dHRN+3jV7/6lbp27aqKigq98cYbOnv2rFwulzwej+bNm6ennnqq1ccFAACcwUjBSUlJUUlJSaDgHDx4UOnp6dq/f3+g4Bw9elRJSUlq3769ZsyYodmzZ9+yn6tXr+rZZ5/VD3/4Q61cuVIul0vnzp3TzJkzFRERoW9961utOi4AAOAMRk5RpaSk6MSJE2psbJR0o+DMnTtXVVVVKi8vlyQVFxcrLS2tyf389re/VVJSkjIzM+VyuSRJ/fr107p16/Too48+1DEAAADnMrKC07t3b3Xo0EHnz59X9+7ddfHiRQ0aNEgpKSk6cOCAZsyYoeLiYs2cOVMff/yxNm/erMLCwsDnn3vuOU2ePFmlpaUaPnz4Lfv/+te/flc5ampq5PV6H9i4nMjn81k/RttwzIIPd+UAzbufea2pefFO3z9jd1F9cZrqkUce0bBhwxQWFqb09HRt27ZNTz31lFwul/r06SNJdzxF5XK55Pf7W5zB4/FYPzF5vV7rx2gbjhkAG93PvNaSedHYXVRfnKY6dOhQ4FTUk08+Ka/Xe1enpyRp0KBBOnPmzC3b8/Ly9Otf//oBJwYAAMHCWMEZOnSovF6vjh07FjjNFB4erv79++vtt99Wampqs/uYMmWKjh07psLCwsBKTmlpqdatW6eEhISHmh8AADiXsVNUERERiouLU11dndq3bx/YnpqaqtWrV2vo0KHN7qNTp07aunWrVq9erZycHIWFhSkiIkKvvvoqd1ABABDCXP77uYglyIXCtQ6hMEbbcMyCT1V1jSIjPKZjAI7lq2tQeFt3iz8fVNfgAIAtyssumI6Ae8Bdiq3vfspNS1FwAACAdSg4AADAOhQcAABgHQoOAACwTkjfRXXmzBl5PNz5AABAsGrTpo369u17y/aQLjgAAMBOnKICAADWoeAAAADrUHAAAIB1KDgAAMA6FBwAAGAdCg4AALBOG9MB8PDs27dPe/fu1WuvvSbpxv/78+qrr8rtdis5OVnf+973DCfE7fj9fqWkpCguLk6SNGjQIC1atMhsKNyisbFRy5cv1/nz59WuXTu98sor6tWrl+lYaEZmZqbat28vSerZs6dWrlxpOBHu5E9/+pPWrFmjrVu36tKlS8rOzpbL5VLfvn21bNkyhYU1vUZDwbHUK6+8og8//PCmx8svW7ZM69ev12OPPaa5c+fq7Nmz6t+/v8GUuJ3y8nL1799fv/zlL01HQRN+//vfq7a2Vtu3b9eZM2e0atUqbdiwwXQsNKGmpkaStHXrVsNJ0JyNGzeqsLBQERERkqSVK1fqxRdf1NChQ7V06VLt379fo0aNanIfnKKyVFJSkpYvXx54XVlZqdraWsXGxsrlcik5OVnFxcXmAuKOzp49q4qKCk2dOlVz5szRhQsXTEfCbZw8eVLDhw+XdGOVrbS01HAiNOfcuXOqrq7WrFmzNG3aNJ05c8Z0JNxBbGys1q9fH3h99uxZfeMb35AkpaSk6I9//GOz+2AFJ8jl5+dry5YtN21bsWKFxowZo5KSksC2yspKRUVFBV5HRkbq008/bbWcuL3bHb+lS5dq7ty5Gj16tE6cOKGsrCzt3LnTUELcyZe/U263W/X19WrThmnVqcLDwzV79mxNnjxZZWVlmjNnjvbu3csxc6CMjAxdvnw58Nrv98vlckm68ffr2rVrze6DoxrkJk+erMmTJzf7vqioKFVVVQVeV1VVqUOHDg8zGu7C7Y5fdXW13G63JGnIkCGqqKi46csNZ/jyd6qxsZE/lA7Xu3dv9erVSy6XS71791anTp105coVxcTEmI6GZvzv9TZ3+/eLU1QhIioqSm3btlV5ebn8fr8+/PBDDRkyxHQs3MbPf/7zwKrOuXPn1L17d8qNAyUlJenw4cOSblzAn5CQYDgRmrNjxw6tWrVKklRRUaHKykp16dLFcCrcjccffzxwVuLw4cN39feLf26EkJdfflk/+tGP1NDQoOTkZA0cONB0JNzG3LlzlZWVpQ8++EBut5u7PBxq1KhR+sMf/qBnn31Wfr9fK1asMB0JzZg0aZJeeuklfec735HL5dKKFStYdQsSixcv1pIlS/T6668rPj5eGRkZzX6Gp4kDAADrcIoKAABYh4IDAACsQ8EBAADWoeAAAADrUHAAAIB1KDgAAMA6FBwAAGCd/wN/H+D6dcwKowAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 576x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "kelly_allocation[kelly_allocation.abs()>5].sort_values(ascending=False).plot.barh(figsize=(8, 10))\n",
    "plt.yticks(fontsize=12)\n",
    "sns.despine()\n",
    "plt.tight_layout();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Performance vs SP500"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Kelly rule does really well. But it has also been computed from historical data.."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-17T16:14:31.475960Z",
     "start_time": "2020-06-17T16:14:30.579302Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = monthly_returns.loc['2010':].mul(kelly_allocation.div(kelly_allocation.sum())).sum(1).to_frame('Kelly').add(1).cumprod().sub(1).plot(figsize=(14,4));\n",
    "sp500.filter(monthly_returns.loc['2010':].index).pct_change().add(1).cumprod().sub(1).to_frame('SP500').plot(ax=ax, legend=True)\n",
    "plt.tight_layout()\n",
    "sns.despine();"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.7"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": true,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": true
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
